The book consists of thirty lectures on diverse topics, covering much of the mathematical
landscape rather than focusing on one area. The reader will learn numerous results that …

The subject of Discrete Geometry and Convex Polytopes has received much attention in
recent decades, with an explosion of the work in the field. This book is an introduction …

Решением многогранников, по аналогии с термином “решение треугольников”, мы
называем теорию и методы вычисления одних геометрических параметров …

A simple path or cycle in a triangulated surface is normal if it intersects any triangle in a finite
set of arcs, each crossing from one edge of the triangle to another. We describe an algorithm …

We study wrappings of smooth (convex) surfaces by a flat piece of paper or foil. Such
wrappings differ from standard mathematical origami because they require infinitely many …

Motivated by the methods and results of manifold sampling based on Ricci curvature, we
propose a similar approach for networks. To this end, we make an appeal to three types of …

We explore the practicability of Nash's Embedding Theorem in vision and imaging sciences.
In particular, we investigate the relevance of a result of Burago and Zalgaller regarding the …

Consider the surface S of a unit cube C in R3. Think of S being a container made of
cardboard and full of water. Now, can one add more water into the container? In other …

We show that any compact, orientable, piecewise-linear two-manifold with Euclidean metric
can be realized as a flat origami, meaning a set of non-crossing polygons in Euclidean 2 …

We prove that all polyhedral surfaces in R3 have volume-increasing isometric deformations.
This resolves the conjecture of Bleecker who proved it for convex simplicial surfaces [B1]. A …